Controllers (control systems) are ubiquitous in industry. A purpose of a controller is to solicit an actual response of a system that is to be controlled (conventionally called the plant) to match a desired response (called the reference signal or command signal).
There are many different measures of merit that are commonly used for controllers. For example, it is common to want to minimize the time required to bring about the desired response of the plant. For example, the occupant of a chilly room may set a thermostat to request that the room temperature be raised to 70 degrees. The reference signal is 70 degrees. The controller causes fuel to flow into the furnace so as to cause the furnace to heat the room to 70 degrees. As the temperature of the room is rising, the controller may measure the difference between the reference signal (the desired temperature) and the room's actual temperature (the plant response). The measure of merit for this controller may be based on the amount of time it takes to warm the room to the desired temperature.
The measure of merit for a controller typically involves several different (and usually conflicting) considerations. For example, in addition to wanting to minimize the time required to bring about the desired change in the plant, it is also common to simultaneously want to avoid significantly overshooting the desired values for the plant response. For example, although the occupant wants the temperature to reach 70 degrees quickly, he doesn't want to accomplish this goal by first raising the temperature to 110 degrees (overshooting the reference signal) and then letting the room cool to the desired 70 degrees. In fact, it would be ideal if the temperature quickly rose to 70 degrees without any overshoot above 70 degrees.
The cost of energy is often a major additional competing consideration in measuring the merit of a controller. Different strategies for causing a plant to reach a desired state generally have a different cost in terms of the cost of energy. Thus, the measure of merit for a controller may consist of a specified mixture reflecting the time required to bring about the desired change in the plant, the energy required to effect the change, and the avoidance of overshoot.
In addition to the above considerations, it is common to place certain practical limits on the value of the control variable(s) so that the plant is not presented with extreme values for the control variable(s). For example, a limiter would prevent a control variable from heating the room to 110 degrees. Similarly, it is common to place certain practical limits on the plant's internal state variables so that they do not exceed certain prespecified limits.
Furthermore, since all real world plants and controllers are imperfect devices, it is also desirable that a controller operate robustly in the face of perturbations or disturbances in the actual behavior of the plant or controller. It is also desirable to suppress and ignore high frequency noise in the reference signal, the control variable, and the actual plant response.
Real-world controllers must consider the fact that the actual value of a control variable must be finite (e.g., cannot be an impulse of infinite amplitude) and that real-world plants do not respond instantaneously.
Many, if not most, real-world controllers are operated manually. However, the focus here is on automatic controllers—that is, controllers that automatically process reference signal(s) and plant output(s) (and possibly other inputs) in order to create the control signals.
The underlying principles of controllers are broadly the same whether the system is mechanical, electrical, thermodynamic, hydraulic, biological, economic, etc. and whether the variable of interest is temperature, velocity, voltage, water pressure, interest rates, heart rate, humidity, etc. Moreover, many controllers incorporate elements from several different engineering domains. For example, the variable of interest for a home heating system is temperature, the setting of the thermostat and the room's current temperature are usually converted into an electrical signal, these electrical signals are usually processed by an electrical controller (analog or digital), the control mechanism is usually a mechanical valve that permits oil to flow into the furnace, while the furnace is a thermodynamic system.
In spite of the multidisciplinary aspects of control engineering, there are several reasons why it is often convenient to discuss controllers in purely electrical terms. First, many real-world sensors, reference signals, control variables, and controllers are, in fact, electrical. Second, regardless of whether the controller or plant is actually electrical, control engineers often use electrical terminology as a common language for modeling plants and controllers. Third, it is possible to use electrical simulators, such as the SPICE simulator (described in SPICE 3 Version 3F5 User's Manual by Thomas Quarles, A. R. Newton, D. O. Pederson, and A. Sangiovanni-Vincentelli, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Calif.:1994) for solving control problems. Electrical simulators are useful because the systems of simultaneous integro-differential equations used in electrical engineering also apply to many aspects of control engineering.
Design is a major activity of practicing engineers. Engineers are often called upon to design controllers that satisfy certain prespecified high-level design goals. The creation of a design for a complex structure, such as a controller, typically involves intricate tradeoffs between competing considerations. Design is ordinarily thought to require human intelligence.
Controllers can be composed of a variety of types of one or more signal processing blocks that process signals in the time-domain, including, for example, but not limited to, gain, lead, lag, integrator, differentiator, adder, inverter, subtractor, and multiplier. Each of these processing blocks has one or more inputs and a single output. The input to a controller typically consists of the reference signal(s) and the plant response(s) or, sometimes, just the difference (error) between each reference signal and the corresponding plant response. The output of a controller consists of control variable(s) that are passed to the plant.
One or more parameter values are required to completely specify many of the signal processing blocks used in controllers. For example, the complete specification of a gain block requires specification of its amplification factor (e.g., 100-to-1 or 40 decibel amplification). The specification of these parameter values (which are typically numerical values) is sometimes called the “sizing.”
The individual signal processing blocks of a controller are coupled to one another in a particular topological arrangement. The topology of a controller entails the specification of the total number of processing blocks to be employed in the controller, the type of each block (e.g., gain, lead, lag, integrator, differentiator, adder, inverter, subtractor, and multiplier), and the connections between the input point(s) and the output point of each block in the controller.
The design (e.g., synthesis) of a controller requires specification of both the topology and parameter values (sizing) such that the controller satisfies certain user-specified high-level design requirements.